Help with Mathematical Solution to a Single Leg Hanging Basket

AI Thread Summary
The discussion revolves around the dynamics of a single leg hanging basket, focusing on the relationship between the center of gravity (CG), the lifting point (ML), and the pivot point (P). It is emphasized that for stability, the CG should ideally be directly beneath the lifting point to minimize gravitational potential energy and avoid net torque. Participants debate the implications of fixed points F, G, and P, questioning whether the CG can deviate from this vertical alignment without causing movement. The necessity of additional dimensions for accurate calculations is highlighted, as the angle (θ) cannot be determined without knowing the distances involved. Overall, the conversation underscores the importance of geometry in maintaining balance in the system.
James Hayes
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Picture a basket, connected to a hanging point (ML), from two fixings (F). One of these ropes connecting these points snaps, and the basket shifts and drops on one side. Resulting in the rope snagging onto a pivot point (P). We know the mass, the length of a couple dimensions. I want to know a method of calculating the angle theta, shown in the last diagram. Point F and G and P are all fixed in place and do not move. Please see PDF for more information.
1610704478272.png
1610704519940.png
 

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Hello @James Hayes , :welcome: !

Is this homework or do you consider designing a balloon with basket ?

James Hayes said:
the basket shifts and drops on one side. Resulting in the rope snagging onto a pivot point (P)
And if nothing dampens the swinging ?
(I find the "Point F and G and P are all fixed in place" pretty questionable for G !)

Never mind, I suppose you silently assume the swinging terminates, at which time G should be directly underneath ML. Right ?

PFG is a triangle that keeps its shape, but rotates. How far is undeteermined since you give no sideways distances. Additionally, ##\theta## can not be calculated as long as ML to P is unknown
 
Hi

F, G and P are fixed. But surely the center of gravity does not need to be directly underneath the lifting point ML. The black line from ML to P to F is a rope, it does not 'fix' to P, it simply is wrapped around P. Surely, the tension in the rope pulling on fixing point 'F', around pivot point p will cause the center of gravity to shift out from being directly underneath, as this creates a force in X from point F.

thank you
 
James Hayes said:
But surely the center of gravity does not need to be directly underneath the lifting point ML.
If it is not, there will be a net torque due to gravity that will cause movement, no?
 
The system will hang such as to minimize the gravitational potential energy. This requires the C M to be directly below the support, as @berkeman man has observed.

These are really small dimensions!
 
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Dr.D said:
These are really small dimensions!
Oh jeeze, I missed that. Especially small considering the mass... :wink:

1610746538408.png
 
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berkeman said:
Oh jeeze, I missed that. Especially small considering the mass... :wink:

View attachment 276314
It is just very high density material!
 
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James Hayes said:
Hi

F, G and P are fixed. But surely the center of gravity does not need to be directly underneath the lifting point ML.
Welcome, James! :cool:

On the contrary, points ML and G must be on the same vertical line.
That vertical line should intersect the line joining P and F somewhere.
That point of intersection depends on dimensions that are not provided by the problem.
For example, x and y distances between G and F or ML and F.
 
It seems to me the rope from ML to P must be vertical in the steady state, otherwise there would be a sideways force on the body and it would swing. Therefore, Theta is zero, and ML, P and G are all on the same line vertically. The angle ML-P-F is determined by geometry.
 

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